Chicken Parmesan, I have an easy question ?

It says crosswise, which means cut across the grain of the meat fibers, across the width. That's because the recipe calls for pounding the meat thinner and to an even thickness, which will make it much longer than a normal serving size for plating if the length isn't cut in half. Pounding the meat is important so that the interior will cook faster, allowing it to get done before overcooking the thin parts of the meat and before burning the crust.